U2 on a Cure forum? RS wouldn't be pleased...
But anyway, these aren't 'typical' U2 songs, so perhaps I could be excused.
The first one is called 'Yoshino Blossom' and is an instrumental outtake from the 'Unforgettable Fire' sessions (1984). It remained unreleased until 2009, when it appeared on the 2nd CD of the remastered deluxe edition of said album. It's a driving and simultaneously rather poignant tune (courtesy of the piano) and it shares some similarities with 'New Years Day' (not a rehash, though):
www.youtube.com/watch?v=W-iXMhy8jKI (http://www.youtube.com/watch?v=W-iXMhy8jKI#ws)
The second is a song called 'Walk to the Water', perhaps my second favourite U2 song ever (the first would be 'Bad'). It was a B-Side to the 'With or Without You' single (1987). Nowadays it can be found on the 2nd CD of the remastered deluxe edition of the 'Joshua Tree' album. Again, not typical U2, part of it is even spoken word and it has a short simple guitar 'solo' that could probably make stones cry...
www.youtube.com/watch?v=1zWXunpRN_M (http://www.youtube.com/watch?v=1zWXunpRN_M#ws)